Lesson 6: Addition and Subtraction - Notes

Lesson 6: Addition and Subtraction

Introduction

Addition often means 'to meet', resulting in a larger quantity.
Examples of addition at home include combining groups (oranges, chapattis).
Focus is on addition of countable items.
Goal: To help children understand that adding groups means finding the total number of items.
Emphasis on understanding concepts and related language.

Objectives

Explain addition and subtraction processes.
Plan and implement activities to teach addition and subtraction.
Explain creating and solving written problems.
Suggest effective ways to explain addition and subtraction algorithms.
Help children develop the ability to estimate sums and differences.
Evaluate teaching methods.

Understanding Addition

Addition should have a concrete context for young children.
Use concrete experiences like:
- Marbles
- Twigs
- Buttons
- Stones
- Biscuits
Encourage children to explain their actions.
Help with questions like:
- "How many marbles did you have?"
- "How many more did I give you?"
- "So how many marbles are there in all?"
Introduce the word 'add' and connect it with the child's actions.
Relate 'add' to grouping and understanding words like 'total' and 'money'.
Write the symbolic representation (e.g., $2 + 3 = 5$ ) after the child verbalizes the addition.
Through examples, children learn symbolic representation and practice.
Children understand properties of pairs (e.g., $3 + 2 = 1 + 4$ ) after combining objects.
If $3 + 2 = 5$ , then $5 = 3 + 2$ .

Example 1: Ms. Mehta's Approach

Ms. Mehta teaches in a government primary school in Delhi.
Children collect and count objects like pebbles.
They make two piles and find the total.
Practice addition through games without explicitly stating they are learning addition.
Game: Dice and Stones
- Two children/teams roll dice and collect stones equal to the number rolled.
- The one with the most stones after two rounds wins.
- Team members say aloud what they are doing.
Picture Cards:
- Show cards in parts (e.g., three sitting birds, then two flying in).
- Ask children to count the total (Figure 1).
Add written text to each card:
- "3 and 2 together make 5"
- "3 and 2 make 5"
- "3 and 2 equals 5"
- $3 + 2 = 5$
Introduce 'plus' and 'equal' with their symbols gradually.
Use pictorial worksheets where children write the additions shown.
Ask questions like $3 + 4 = ?$
Ms. Mehta's three stages for introducing addition:
- Concrete things
- Pictorial presentation
- Symbolic presentation

Word Problems

Word problems are important for attaching meaning to abstract addition.
Example: Asking a child how many chapattis are needed in a context related to their world, not abstract sums.
Word questions should be introduced early, not after learning basic facts.
Example: Mita had two tennis balls, and a friend brought three. Mita knew she had five balls.
Ask questions related to the child’s world, such as adding marbles from different piles.

Types of Word Problems

Aggregation: Combining quantities to form one quantity.
- Example: Munni has 3 pencils, Munna has 2; how many pencils in total?
Augmentation: Increasing a quantity by a certain amount.
- Example: 5 bottles in a bag, 4 more added; how many bottles now?
Assessment: Check understanding with concrete/picture-based activities and asking them to create word problems.

Understanding Subtraction

Subtraction is the reverse of addition.
It involves making a collection smaller by removing items.
Subtraction is more difficult because it requires recognizing which quantity to eliminate.
Subtraction is not commutative: $9 - 3 <br /> eq 3 - 9$

Types of Word Problems (Subtraction)

Division: Taking out things and finding the remainder.
- Example: 15 toffees, 10 eaten; how many left?
Finding the deficiency: Finding how much has been removed.
- Example: 15 toffees, now 5 left; how many eaten?
Comparison: Finding the difference between two groups.
- Example: Munna has 15 erasers, Munni has 5; how many fewer does Munni have?
Complementary addition: Finding how much to add to reach another number.
- Example: Class seats 50, 20 seated; how many more can sit?
Children find complementary addition most difficult, often associating 'and' with addition.
Some children convert subtraction problems into complementary addition problems.
Example: 'Subtract 7 from 13' becomes 'what will be added to 7 to get 13?'

Teaching Subtraction

Introduce subtraction with familiar objects.
Example: Subtract 3 laddus from 5 laddus.
Repeat language associated with the action (taking away).
Use stories and games with subtraction words.
Example story: Raju invited 9 friends, but 2 couldn't come, so 7 came.
Subtraction games: Divide children into groups; one group states a subtraction fact, the other makes a word problem.
Number strips help practice counting backwards.
- Subtracting 4 from 9 means counting back 4 squares from 9 on the number strip (Figure 3).
Introduce the 'minus' symbol (-) and have children use it repeatedly.
Use real objects, vertical lines, crossing out, or number strips as aids.

Relationship Between Addition and Subtraction

Children need experiences involving both addition and subtraction.
After adding familiar objects, introduce subtraction.
Relate operations with activities like giving and taking away laddus.
Introduce pictorial representations of addition and subtraction (Figures 4 and 5).
Use pictorial worksheets for practice (Figure 6).
Ask children to represent facts like $6 - 4 = 2$ using objects or pictures.
Solve word problems related to children's world.

Sequencing Addition and Subtraction

1. "Subtraction should be discussed only after addition has been learned."
2. "It is more beneficial to teach addition and subtraction together."

Developing Fluency

Children progress slowly from concrete/pictorial to abstract stages.
They need repeated practice with concrete things or pictures.
Provide meaningful contexts like decorating, exchanging money, or travelling.
Use games like marbles or Ludo.
Be patient, give time to understand, and let them speak about the process.
Caution against written problems that are too complicated or out of touch with the child's world.
Introduce written problems with simple, thoughtful words from the beginning.
Addition-type problems can be introduced later than aggregation-type problems.

Algorithm Problems

Children often mechanically apply algorithms without understanding.
This leads to mistakes.
Mistakes can arise from:
- Not understanding the operation.
- Not understanding how to write two-digit or more numbers.
- Not understanding regrouping.
- Lack of clear concept of 'zero'.
Address this by:
- Using methods to help children learn operations and language.
- Helping them to learn the concept of ‘borrowing’.
Example 3: Playing a game with cardboard pieces to represent units, tens, hundreds.
- Black = units
- Yellow = tens
- Red = hundreds

Developing Guessing Skills

Children need to develop the ability to estimate answers.
Important for daily life (shopping, budgeting) and catching mistakes.
Study Example: Children given addition problems, and the answers were way off and the children did not realize it.
Rounding off numbers for easier mental calculation.
- $1821 + 695 + 250$ becomes $1800 + 700 + 300$
Estimate based on leftmost digit, then adjust using remaining digits.

Example 4: Sheela's Approach

Sheela helps Raju correct his addition mistakes by asking if the answer makes sense.
She uses bundles of sticks to represent tens and loose sticks for units.
She asks if the total will be more than a certain number.
She guides him to estimate by adding the tens digits first.
She reinforces that no number can have more than 9 units.
She helps him use guesswork to check answers.
She gives problems asking for both approximate and exact answers.
She emphasizes continuous practice.

Summary

Explained meaning of addition and subtraction.
Discussed word problem types.
Emphasized starting word problems early.
Addressed mistakes in algorithms.
Explained 'gain' and 'borrow'.
Developed estimation abilities.